3(x-5)(2x+1)=0

Solution for 3(x-5)(2x+1)=0 equation:

3(x-5)(2x+1)=0

We multiply parentheses ..

3(+2x^2+x-10x-5)=0

We multiply parentheses

6x^2+3x-30x-15=0

We add all the numbers together, and all the variables

6x^2-27x-15=0

a = 6; b = -27; c = -15;
Δ = b2-4ac
Δ = -272-4·6·(-15)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-33}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*6}=\frac{60}{12}
=5
$